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<title>Problem 2356. -- 不等式 -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>2356: 不等式</h2><span class=green>Time Limit: </span>3 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>128 MB<br><span class=green>Submit: </span>43&nbsp;&nbsp;<span class=green>Solved: </span>18<br>[<a href='submitpage.php?id=2356'>Submit</a>][<a href='problemstatus.php?id=2356'>Status</a>][<a href='bbs.php?id=2356'>Discuss</a>]</center><h2>Description</h2><div class=content><div style="text-indent: 24.1pt"><span style="font-size: 12pt">数学中有很多不等式，比如，当</span><span style="font-size: 12pt">x,y&gt;0</span><span style="font-size: 12pt">时：</span></div>
<div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">x<sup>2</sup>+y<sup>2</sup>&ge;2xy</span></div>
<div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">x<sup>3</sup>+y<sup>3</sup>&ge;x<sup>2</sup>y+xy<sup>2</sup></span></div>
<div style="text-indent: 24.1pt"><span style="font-size: 12pt">输入两个分别齐次且系数非负的二元多项式</span><span style="font-size: 12pt">f(x,y)</span><span style="font-size: 12pt">和</span><span style="font-size: 12pt">g(x,y)</span><span style="font-size: 12pt">，判断是否存在</span><span style="font-size: 12pt">A,r&gt;0</span><span style="font-size: 12pt">，满足对于任意</span><span style="font-size: 12pt">x,y&gt;0</span><span style="font-size: 12pt">，都有：</span></div>
<div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">f(x,y)&ge;A*[g(x,y)]<sup>r</sup></span></div></div><h2>Input</h2><div class=content><div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">包含多组数据，相邻两组数据之间用一个空行隔开。</span></div>
<div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">每组数据包含两行</span><span style="font-size: 12pt; line-height: 200%">.</span></div>
<div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">第一行包括</span><span style="font-size: 12pt; line-height: 200%">n+2</span><span style="font-size: 12pt; line-height: 200%">个非负整数，</span><span style="font-size: 12pt; line-height: 200%">n,a<sub>0</sub>,a<sub>1</sub>,&hellip;,a<sub>n</sub></span><span style="font-size: 12pt; line-height: 200%">，</span><span style="font-size: 12pt; line-height: 200%">a<sub>i</sub></span><span style="font-size: 12pt; line-height: 200%">不全是</span><span style="font-size: 12pt; line-height: 200%">0.</span><span style="font-size: 12pt; line-height: 200%">表示</span><span style="font-size: 12pt; line-height: 200%">f(x,y)=a<sub>0</sub>x<sup>n</sup>+a<sub>1</sub>x<sup>n-1</sup>y+&hellip;&hellip;+a<sub>n</sub>y<sup>n</sup>.</span></div>
<div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">第二行包括</span><span style="font-size: 12pt; line-height: 200%">m+2</span><span style="font-size: 12pt; line-height: 200%">个非负整数</span><span style="font-size: 12pt; line-height: 200%">，</span><span style="font-size: 12pt; line-height: 200%">m,b<sub>0</sub>,b<sub>1</sub>,&hellip;,b<sub>m</sub></span><span style="font-size: 12pt; line-height: 200%">，</span><span style="font-size: 12pt; line-height: 200%">b<sub>i</sub></span><span style="font-size: 12pt; line-height: 200%">不全是</span><span style="font-size: 12pt; line-height: 200%">0.</span><span style="font-size: 12pt; line-height: 200%">表示</span><span style="font-size: 12pt; line-height: 200%">g(x,y)=b<sub>0</sub>x<sup>m</sup>+b<sub>1</sub>x<sup>m-1</sup>y+&hellip;&hellip;+b<sub>m</sub>y<sup>m</sup>.</span></div></div><h2>Output</h2><div class=content><div style="text-indent: 24.1pt; line-height: 200%"><span style="font-size: 12pt; line-height: 200%">对于每组数据，输出一行，若存在则输出</span><span style="font-size: 12pt; line-height: 200%">&rdquo;YES&rdquo;</span><span style="font-size: 12pt; line-height: 200%">，否则输出</span><span style="font-size: 12pt; line-height: 200%">&rdquo;NO&rdquo;.</span></div></div><h2>Sample Input</h2>
			<div class=content><span class=sampledata>1 1 1<br />
2 0 1 0<br />
 <br />
2 1 1 1<br />
3 1 0 0 1<br />
 <br />
5 1 0 0 1 0 0<br />
5 0 0 1 0 0 1<br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata>YES<br />
YES<br />
NO<br />
</span></div><h2>HINT</h2>
			<div class=content><p><p>【样例说明】<br /><br />
数据1：x+y&ge;2[(xy)1/2]；<br /><br />
数据2：x2+xy+y2&ge;(x3+y3)2/3，展开易证；<br /><br />
数据3：反设x5+x2y3&ge;A*(x3y2+y5)r，对于所有正数x,y成立.取x=y，得：2x5&ge;A(2x5)r，若r&gt;1,则x取足够大时不等式不成立，若r&lt;1,则x取足够小时不等式不成立，所以r=1；<br /><br />
再取x=1，得：1+y3&ge;A*(y2+y5)，即：1&ge;Ay2，不可能对所有正数y成立，故不存在A,r.<br /><br />
【数据规模】<br /><br />
最多包含100组数据，且1&lt;=n,m&lt;=100，系数大小不超过10000.</p></p></div><h2>Source</h2>
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